Generalized Contraction Mapping Principle in Intuitionistic Menger Spaces and an Application to Differential Equations
-
摘要: 利用Atanassov的思路,将直觉Menger空间定义为由Menger提出的Menger空间的自然推广.同时也得出一个新广义压缩映射,并运用该压缩映射证明了直觉Menger空间中微分方程解的存在性定理.
-
关键词:
- 广义压缩映射 /
- 直觉Menger空间 /
- 直觉Menger赋范空间 /
- 直觉概率有界集
Abstract: Using the idea of Atanassov,the notion of intuitionistic Menger spaces was defined as a natural generalizations of Menger spaces due to Menger.A new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces were obtained. -
[1] Menger K. Statistical metric spaces[J].Proc Nat Acad Sci,1942,28:535-537. doi: 10.1073/pnas.28.12.535 [2] Schweizer B,Sklar A. Statistical metric spaces[J].Pacific J Math,1960,10(1):313-334. [3] Schweizer B,Sklar A.Probabilistic Metric Spaces[M].New York:North-Holland,1983. [4] Schweizer B, Sklar A,Thorp E. The metrization of statistical metric spaces[J].Pacific J Math,1960,10:673-675. [5] Chang S S, Lee B S,Cho Y J,et al.Generalized contraction mapping principle and differential equations in probabilistic metric spaces[J].Proceedings of the American Mathematical Society,1996,124(8):2367-2376. doi: 10.1090/S0002-9939-96-03289-3 [6] Hadzic O,Pap E.Fixed Point Theory in Probabilistic Metric Spaces[M].Dordrecht:Kluwer Acad Pub,2001. [7] Hadzic O, Pap E,Radu V. Generalized contraction mapping principles in probabilistic metric spaces[J].Acta Math Hungar,2003,101(1/2):131-148. [8] Mihet D. On the contraction principle in Menger and non-Archimedean Menger spaces[J].An Univ Timisoara Ser Mat Inform,1994,32(2):45-50. [9] Klement E P, Mesiar R,Pap E.Triangular Norms[M].Trends in Logic 8.Dordrecht:Kluwer Acad Pub,2000. [10] Radu V.Lectures on Probabilistic Analysis[M].West University of Timisoara, 1996. [11] Radu V. Some remarks on the probabilistic contractions on fuzzy Menger spaces[A/J]. In:The Eighth Internat Conf on Applied Mathematics and Computer Science[C].Cluj-Napoca, 2002;Automat Comput Appl Math,2002,11(1):125-131. [12] Kramosil O,Michalek J. Fuzzy metric and statistical metric spaces[J].Kybernetica,1975,11:326-334. [13] George A,Veeramani P. On some results in fuzzy metric spaces[J].Fuzzy Sets and Systems,1994,64:395-399. doi: 10.1016/0165-0114(94)90162-7 [14] Mihet D. A Banach contraction theorem in fuzzy metric spaces[J].Fuzzy Sets and Systems,2004,144:431-439. doi: 10.1016/S0165-0114(03)00305-1 [15] Park J H. Intuitionistic fuzzy metric spaces[J].Chaos, Solitons & Fractals,2004, 22:1039-1046. [16] Kelley J L.General Topology[M].Princeton, 1955. [17] Atanassov K.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20:87-96. doi: 10.1016/S0165-0114(86)80034-3
点击查看大图
计量
- 文章访问数: 2385
- HTML全文浏览量: 55
- PDF下载量: 757
- 被引次数: 0